Cavity resonators are hollow closed conductors, such as metal boxes or cavities provided within metal enclosures, which may contain electromagnetic waves reflecting back and forth between the cavity's walls. For devices referred to by the term “cavity resonators,” these waves are most often radio waves or microwaves. When a source of radio waves or microwaves (or, in some instances, other forms of electromagnetic energy) that is at one of the cavity's resonant frequencies is applied, the oppositely-moving waves form standing waves, and the cavity stores electromagnetic energy. Microwaves are often most practical for this purpose, because the cavity's lowest resonant frequency is the frequency at which the width of the cavity is equal to a half-wavelength, meaning that cavities that make use of longer-wavelength radio waves can often be oversized.
Cavity resonators also exist for other parts of the electromagnetic spectrum. Optical resonators, also called optical cavities or resonating cavities, are arrangements of highly reflective mirrors or reflective material that form standing-wave cavity resonators for light waves, such as IR waves, visible light waves, or UV waves. Optical resonators are a major component of lasers, and may be disposed around the lasing medium in order to provide feedback for the laser light. Light that is confined in a resonator will reflect multiple times from the mirrors in a manner that tends to form stable patterns or frequencies. (Only certain patterns or frequencies will typically be produced, with others being suppressed by destructive interference.)
The efficiency of a laser, or other resonator-based system, is described by the gain coefficient, which specifically describes the ability of a laser medium to increase optical power. Certain losses may be associated with elements of the resonator system which can reduce the gain of the laser or otherwise impair efficiency. Specifically, losses may be associated with transmission of light at the resonator mirrors, absorption and scattering by the mirrors, absorption by the laser medium, and diffraction losses at the mirrors. Each of these losses may contribute, in some manner, to reduction of the overall gain coefficient.
An important concept is the “round trip gain” of the resonator, which may determine whether the output power of the laser or other resonator device may increase, decrease, or remain constant, based on losses or amplifications that the light beam may have in a complete round trip through the laser. (When the round trip gain G is greater than 1, the oscillations in the resonator will grow, while when the round trip gain G is less than 1, the oscillations in the resonator will die out.) As the laser light completes this loop, from a mirror on one side of the resonator to a mirror on the other side of the resonator and back again, some of the light may be transmitted through each mirror and may exit the cavity. (In lasers, this transmitted light may form the beam.) Round trip gain may be a ratio of the intensity of radiation at the end of the loop to the intensity of radiation at the beginning of the loop. This value may be determined by the volume losses in the laser or other resonator, and by the losses in the form of useful output supplied through the mirrors.
Specifically, round trip gain G may be provided as:
  G  =                    Final        ⁢                                  ⁢        irradiance                    Initial        ⁢                                  ⁢        irradiance              =                                        I            0                    *                      R            1                    *                      e                                          (                                  k                  -                  γ                                )                            ⁢              L                                *                      R            2                    *                      e                                          (                                  k                  -                  γ                                )                            ⁢              L                                                I          0                    =                                    I            0                    ⁢                      R            1                    ⁢                      R            2                    ⁢                      e                          2              ⁢                              (                                  k                  -                  γ                                )                            ⁢              L                                                I          0                    
with I0 representing the initial irradiance value, R1 representing the reflectivity of the first reflector, R2 representing the reflectivity of the second reflector, and e(k-γ)L representing the change in the beam irradiance each time the beam passes through the lasing medium. γ may represent the effective volume loss coefficient, while k, or kth, may be the threshold gain coefficient, given as a function of the length of the lasing medium L, R1 and R2, and γ. (Specifically,
            k      th        =          γ      +                        1                      2            ⁢            L                          ⁢        ln        ⁢                              1                                          R                1                            ⁢                              R                2                                              .                      )